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Phenology: the timing of biological events (life stages such as flowering, fruiting, bird arrival underpins or influences many different ecological processes.) These processes also have a significant role in shaping society’s values (e.g. on human health, biodiversity, forestry, agriculture and tourism. Since the 1990s, primarily because of climate change phenological time series have been used to determine and report the impacts of global warming in both natural and managed systems. Determining trends in relation to long-term climate, however, is not easy as trends can be confounded by short-term interannual trends. Hence not only are long term records required, but also needed is the development of novel statistical methods which can deal with confounding factors. Wavelet methods have been extensively applied to many arenas (eg. to the study of change in European spring temperatures and rainfall, changes in vegetation cover, and to brain imaging. It is the ability of wavelets to cope with nonstationary data: to deconstruct a time series into its subcomponents and remove noise; to accommodate multi-scale information, and to minimize correlation and time-dependency in data that have added to their popularity. As phenological time series are usually non-stationary and noisy, and as such wavelet methods present as a useful analytic method for examining phenological records and for the determination of possibly changing climatic impacts on flowering, at an annual and across years basis. The utility of wavelets in investigating the relationship of flowering to climate (three temperature variants and rainfall) is shown in this chapter by examining the flowering intensity time series records of eight Australian eucalypts – namely, E. camaldulensis, E. goniocalyx, E. leucoxylon, E. macrorhyncha, E. melliodora, E. microcarpa, E. polyanthemos and E. tricarpa. This work builds on an initial study by Kang et al. and on the early premise of Hudson et al. that wavelets per se could add integrity to the use of phenological records to detect climate change. This premise was recently confirmed by a study of 4 of the 8 Eucalypt species studied in this chapter by Hudson et al. The discrete wavelet transform (DWT), following the development of Percival and Walden and the maximal overlap DWT (MODWT) is applied in this chapter. The rationale for this approach is that, given the resultant MODWT coefficients, the original (flowering) time series could be reconstructed as an additive decomposition - known as a multiresolution analysis (MRA) and also that the individual detail (sub-component) series could be examined. The aim of this research is to demonstrate the utility of wavelet analysis in phenology by extending the recent work of Hudson et al., from four to eight eucalypt species. This chapter contributes significantly to our understanding of the interplay between climate and the flowering of Eucalyptus flowering – a major southern hemisphere genus

Wavelet Signatures of Climate and Flowering: Identification of Species Groupings